Respuesta :

adebayodeborah8

Answer:

y = 2

Step-by-step explanation:

from the question which says that y is directly proportional to the positive square root of x can be expressed mathematically by saying

y ∝ √x

y = k√x..................................................... where k is the constant of proportionality.

y = 12, x = 9 , k = ?

from

y = k√x

12 = k√9

12 =3k

divide both sides by the coefficient of k which is 3

12/3 = 3k/3

4 = k

therefore K = 3

now, to find the value of y when x = 1/4

from y = k√x

y = 4√1/4

y = 4 × 1/2

y = 2

therefore the value of y when x = 1/4  in this expression y = k√x  is 2

To remove proportionality sign, a proportionality constant is multiplied.

When x = 1/4 then y = 2.

Since, y is directly proportional to the positive square root of x.

So,    [tex]y=k\sqrt{x}[/tex]  , where k is proportionality constant.

Since,  When x = 9, y = 12.

            [tex]12=k\sqrt{9}\\\\k=\frac{12}{3}=4[/tex]

Thus, function become,   [tex]y=4\sqrt{x}[/tex]

To find y, when x = 1/4

        [tex]y=4\sqrt{\frac{1}{4} } \\\\y=4*\frac{1}{2}=2[/tex]

Learn more:

https://brainly.com/question/17689910

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